Your questions pertains to MBA programs and there are some helpful pointers above. You should always confirm with programs, if possible. Generally, it is possible to take the exam just before before the deadlines, but there are exceptions.
Requirements will be somewhat different for non-MBA programs. For example, PhD programs differ in their requirements. It is generally safe to indicate the test date that will fall before the deadline.
There are variations. Some programs need to receive the complete official scores by the deadline. Some others will be fine with incomplete scores. Usually, the AWA score will be incomplete and since these programs tend to mainly look at the Q and V scores, having an incomplete AWA score may not result in dismissal of the application. If possible, self report the scores you have available.
However, if either the admission committees meet very soon after the deadlines or they look at applications on rolling basis, incomplete applications will be at disadvantage. Please be aware of the differences in programs.